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Computer Science > Machine Learning
Title: Data driven modeling for self-similar dynamics
(Submitted on 12 Oct 2023 (v1), last revised 25 Mar 2024 (this version, v3))
Abstract: Multiscale modeling of complex systems is crucial for understanding their intricacies. Data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. On the other hand, self-similarity is prevalent in complex systems, hinting that large-scale complex systems can be modeled at a reduced cost. In this paper, we introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge, facilitating the modeling of self-similar dynamical systems. For deterministic dynamics, our framework can discern whether the dynamics are self-similar. For uncertain dynamics, it can compare and determine which parameter set is closer to self-similarity. The framework allows us to extract scale-invariant kernels from the dynamics for modeling at any scale. Moreover, our method can identify the power law exponents in self-similar systems. Preliminary tests on the Ising model yielded critical exponents consistent with theoretical expectations, providing valuable insights for addressing critical phase transitions in non-equilibrium systems.
Submission history
From: Ruyi Tao [view email][v1] Thu, 12 Oct 2023 12:39:08 GMT (2069kb,D)
[v2] Fri, 27 Oct 2023 05:25:49 GMT (4134kb,D)
[v3] Mon, 25 Mar 2024 06:21:37 GMT (9683kb,D)
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